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ICSE Class 9 Answered

ABCD is a square .E and F are the midpoints of Sides AB and AD respectively.Prove that area of triangle CEF is equal to 3/8 the area of square ABCD.
Asked by rkarim957 | 22 Oct, 2019, 08:35: PM
answered-by-expert Expert Answer
Let a be the length of each side of square ABCD
rightwards double arrow A E equals a over 2 equals E B space a n d space A F equals a over 2 equals F D A left parenthesis square A B C D right parenthesis equals a squared A left parenthesis triangle A E F right parenthesis equals 1 half cross times A E cross times A F equals a squared over 8 A left parenthesis triangle B E C right parenthesis equals 1 half cross times B E cross times B C equals a squared over 4 A left parenthesis triangle F D C right parenthesis equals 1 half cross times C D cross times F D equals a squared over 4 N o w comma space A left parenthesis square A B C D right parenthesis equals A left parenthesis triangle A E F right parenthesis plus A left parenthesis triangle B E C right parenthesis plus A left parenthesis triangle F D C right parenthesis plus A left parenthesis triangle C E F right parenthesis rightwards double arrow A left parenthesis triangle C E F right parenthesis equals space A left parenthesis square A B C D right parenthesis minus open square brackets A left parenthesis triangle A E F right parenthesis plus A left parenthesis triangle B E C right parenthesis plus A left parenthesis triangle F D C right parenthesis close square brackets rightwards double arrow A left parenthesis triangle C E F right parenthesis equals space a squared minus open square brackets a squared over 8 plus a squared over 4 plus a squared over 4 close square brackets equals fraction numerator 3 a squared over denominator 8 end fraction equals 3 over 8 A left parenthesis square A B C D right parenthesis
Answered by Renu Varma | 24 Oct, 2019, 02:22: PM

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